Here is what the Catechism says about private revleations:
CCC 67: Throughout the ages, there have been so-called “private” revelations, some of which have been recognized by the authority of the Church. They do not belong, however, to the deposit of faith. It is not their role to improve or complete Christ’s definitive Revelation, but to help live more fully by it in a certain period of history. Guided by the Magisterium of the Church, the sensus fidelium knows how to discern and welcome in these revelations whatever constitutes an authentic call of Christ or his saints to the Church.
Christian faith cannot accept “revelations” that claim to surpass or correct the Revelation of which Christ is the fulfillment, as is the case in certain non-Christian religions and also in certain recent sects which base themselves on such “revelations”.
The Congregation of the Doctrine of the Faith gives a pretty good explanation of private revelation in their commentary on the Message of Fatima (scroll down about 2/3 of the way to the “Theological Commentary” section). Here’s probably the most helpful portion of that commentary (I have bolded/italicized the parts I think are especially helpful):
This clarifies two things:
The authority of private revelations is essentially different from that of the definitive public Revelation. The latter demands faith; in it in fact God himself speaks to us through human words and the mediation of the living community of the Church. Faith in God and in his word is different from any other human faith, trust or opinion. The certainty that it is God who is speaking gives me the assurance that I am in touch with truth itself. It gives me a certitude which is beyond verification by any human way of knowing. It is the certitude upon which I build my life and to which I entrust myself in dying.
Private revelation is a help to this faith, and shows its credibility precisely by leading me back to the definitive public Revelation. In this regard, Cardinal Prospero Lambertini, the future Pope Benedict XIV, says in his classic treatise, which later became normative for beatifications and canonizations: “An assent of Catholic faith is not due to revelations approved in this way; it is not even possible. These revelations seek rather an assent of human faith in keeping with the requirements of prudence, which puts them before us as probable and credible to piety”. The Flemish theologian E. Dhanis, an eminent scholar in this field, states succinctly that ecclesiastical approval of a private revelation has three elements: the message contains nothing contrary to faith or morals; it is lawful to make it public; and the faithful are authorized to accept it with prudence (E. Dhanis,Sguardo su Fatima e bilancio di una discussione, in La Civiltà Cattolica 104 , II, 392-406, in particular 397). Such a message can be a genuine help in understanding the Gospel and living it better at a particular moment in time; therefore it should not be disregarded. It is a help which is offered, but which one is not obliged to use.